| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 921 - 952 | |
| DOI | https://doi.org/10.1051/m2an/2023011 | |
| Published online | 07 April 2023 | |
Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch IgA
1
Department of Mathematics, University of Oslo, Postboks 1053, Blindern, Oslo 0316, Norway
2
Institute of Numerical Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria
* Corresponding author: stefan.takacs@numa.uni-linz.ac.at
Received:
6
April
2022
Accepted:
2
February
2023
We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes problem have been proposed, often the analysis was restricted to single-patch domains. We focus on one of the simplest approaches, the isogeometric Taylor–Hood element. We show how stability results for single-patch domains can be carried over to multi-patch domains. While this is possible, the stability strongly depends on the shape of the geometry. We construct a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver that does not suffer from that effect. We give a convergence analysis and provide numerical tests.
Mathematics Subject Classification: 76D07 / 65D07 / 65N55
Key words: Stokes equations / Isogeometric Analysis / domain decomposition
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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